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Russian Journal of Nonlinear Dynamics, 2022, Volume 18, Number 3, Pages 423–439
DOI: https://doi.org/10.20537/nd220307
(Mi nd803)
 

Nonlinear physics and mechanics

Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments

O. S. Kotsur, G. A. Shcheglov, I. K. Marchevsky

Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5, str. 1, Moscow, 105005 Russia
References:
Abstract: This paper is concerned with the equation for the evolution of vorticity in a viscous incompressible fluid, for which approximate weak solutions are sought in the class of vortex filaments. In accordance with the Helmholtz theorem, a system of vortex filaments that is transferred by the flow of an ideal barotropic fluid is an exact solution to the Euler equation. At the same time, for viscous incompressible flows described by the system of Navier – Stokes equations, the search for such generalized solutions in the finite time interval is generally difficult. In this paper, we propose a method for transforming the diffusion term in the vorticity evolution equation that makes it possible to construct its approximate solution in the class of vortex filaments under the assumption that there is no helicity of vorticity. Such an approach is useful in constructing vortex methods of computational hydrodynamics to model viscous incompressible flows.
Keywords: weak solution, vortex filament, helicity of vorticity, diffusion velocity, viscosity.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 0705-2020-0047
This work was supported by the Russian Ministry of Science and Higher Education, project 0705-2020-0047.
Received: 20.06.2022
Accepted: 05.08.2022
Bibliographic databases:
Document Type: Article
MSC: 76D05
Language: english
Citation: O. S. Kotsur, G. A. Shcheglov, I. K. Marchevsky, “Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments”, Rus. J. Nonlin. Dyn., 18:3 (2022), 423–439
Citation in format AMSBIB
\Bibitem{KotShcMar22}
\by O. S. Kotsur, G. A. Shcheglov, I. K. Marchevsky
\paper Approximate Weak Solutions to the Vorticity Evolution
Equation for a Viscous Incompressible Fluid
in the Class of Vortex Filaments
\jour Rus. J. Nonlin. Dyn.
\yr 2022
\vol 18
\issue 3
\pages 423--439
\mathnet{http://mi.mathnet.ru/nd803}
\crossref{https://doi.org/10.20537/nd220307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4497546}
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